Finite Group Databasebeta

← Group #125362

Character table — Group #125362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ21222-2-22-2-22-2-220000002i−2i2i2i−2i−2i00002i−2i002-2001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000000000
χ22222-2-22-2-22-2-220000002i−2i2i2i−2i−2i00002i−2i002-200−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000000000
χ23222-2-22-2-22-2-220000002i−2i−2i−2i2i2i00002i−2i00-22001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000
χ24222-2-22-2-22-2-220000002i−2i−2i−2i2i2i00002i−2i00-2200−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000
χ25222-2-22-2-22-2-22000000−2i2i2i2i−2i−2i0000−2i2i00-22001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000
χ26222-2-22-2-22-2-22000000−2i2i2i2i−2i−2i0000−2i2i00-2200−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000000000
χ27222-2-22-2-22-2-22000000−2i2i−2i−2i2i2i0000−2i2i002-2001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000000000
χ28222-2-22-2-22-2-22000000−2i2i−2i−2i2i2i0000−2i2i002-200−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000000000
χ292-2222-2-2-222-2-222-2-22-22200000000-2-22-200002−22−22−22−22−22−22−22−20000000000000000
χ302-2222-2-2-222-2-222-2-22-22200000000-2-22-20000−22−22−22−22−22−22−22−220000000000000000
χ312-2222-2-2-222-2-222-2-22-2-2-20000000022-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ322-2222-2-2-222-2-222-2-22-2-2-20000000022-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ332-2222-2-2-222-2-2-2-222-222200000000-2-2-2200002−22−2−22−222−22−2−22−220000000000000000
χ342-2222-2-2-222-2-2-2-222-222200000000-2-2-220000−22−222−22−2−22−222−22−20000000000000000
χ352-2222-2-2-222-2-2-2-222-22-2-200000000222-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ362-2222-2-2-222-2-2-2-222-22-2-200000000222-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ372-2222-2-2-2-2-22222-2-2-22002i−2i2i−2i2i2i−2i−2i000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ382-2222-2-2-2-2-22222-2-2-22002i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ392-2222-2-2-2-2-22222-2-2-2200−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ402-2222-2-2-2-2-22222-2-2-2200−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ412-2222-2-2-2-2-222-2-2222-2002i−2i2i−2i−2i−2i2i2i000000000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ422-2222-2-2-2-2-222-2-2222-2002i−2i2i−2i−2i−2i2i2i00000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ432-2222-2-2-2-2-222-2-2222-200−2i2i−2i2i2i2i−2i−2i000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ442-2222-2-2-2-2-222-2-2222-200−2i2i−2i2i2i2i−2i−2i00000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ452-22-2-2-2222-22-20000002i−2i00002i−2i2i−2i−2i2i00002-200002ζ−2ζ−2ζ2ζ0000−2ζ32ζ32ζ3−2ζ30000000000000000
χ462-22-2-2-2222-22-20000002i−2i00002i−2i2i−2i−2i2i00002-20000−2ζ2ζ2ζ−2ζ00002ζ3−2ζ3−2ζ32ζ30000000000000000
χ472-22-2-2-2222-22-20000002i−2i0000−2i2i−2i2i−2i2i0000-222ζ−2ζ−2ζ2ζ0000−2ζ32ζ32ζ3−2ζ300000000000000000000
χ482-22-2-2-2222-22-20000002i−2i0000−2i2i−2i2i−2i2i0000-22−2ζ2ζ2ζ−2ζ00002ζ3−2ζ3−2ζ32ζ300000000000000000000
χ492-22-2-2-2222-22-2000000−2i2i00002i−2i2i−2i2i−2i0000-222ζ3−2ζ3−2ζ32ζ30000−2ζ2ζ2ζ−2ζ00000000000000000000
χ502-22-2-2-2222-22-2000000−2i2i00002i−2i2i−2i2i−2i0000-22−2ζ32ζ32ζ3−2ζ300002ζ−2ζ−2ζ2ζ00000000000000000000
χ512-22-2-2-2222-22-2000000−2i2i0000−2i2i−2i2i2i−2i00002-200002ζ3−2ζ3−2ζ32ζ30000−2ζ2ζ2ζ−2ζ0000000000000000
χ522-22-2-2-2222-22-2000000−2i2i0000−2i2i−2i2i2i−2i00002-20000−2ζ32ζ32ζ3−2ζ300002ζ−2ζ−2ζ2ζ0000000000000000
χ5344444444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ55444-4-44-4-4-444-40000000000004-4-440000000000000000000000000000000000000000
χ56444-4-44-4-4-444-4000000000000-444-40000000000000000000000000000000000000000
χ5744-44-4-4-4400004i−4i4i−4i0000000000000000000000000000000000002i−2i2-2000000000000
χ5844-44-4-4-4400004i−4i4i−4i000000000000000000000000000000000000−2i2i-22000000000000
χ5944-44-4-4-440000−4i4i−4i4i0000000000000000000000000000000000002i−2i-22000000000000
χ6044-44-4-4-440000−4i4i−4i4i000000000000000000000000000000000000−2i2i2-2000000000000
χ614-44-4-4-444-44-44000000004-4-4400000000000000000000000000000000000000000000
χ624-44-4-4-444-44-4400000000-444-400000000000000000000000000000000000000000000
χ634-4-44-444-400004i−4i−4i4i00000000000000000000000000000000000000002-22i−2i00000000
χ644-4-44-444-400004i−4i−4i4i0000000000000000000000000000000000000000-22−2i2i00000000
χ654-4-44-444-40000−4i4i4i−4i00000000000000000000000000000000000000002-2−2i2i00000000
χ664-4-44-444-40000−4i4i4i−4i0000000000000000000000000000000000000000-222i−2i00000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.